Jan Stegmann

Eigenfrequency and Buckling Optimization of Laminated Composite Shell Structures Using Discrete Material Optimization

The design problem of maximizing the lowest eigenfrequency or the buckling load factor of laminated composite shell structures is investigated using the so-called Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material, stacking sequence and fiber orientation simultaneously is illustrated for two multi-layered multi-material plate examples.

On Discrete Material Optimization of Laminated Composites Using Global and Local Criteria

Discrete Material Optimization is introduced as a method for doing material optimization on general laminated composite shell structures where the objective is to minimize maximum strain values. The method relies on ideas from multiphase topology optimization and uses gradient information in combination with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method has previously been applied to compliance minimization and its applicability to min-max problems is demonstrated for two simple examples and the results compared to designs obtained using compliance minimization.

Discrete Material Optimization of Laminated Composites: SIMP vs. Global Optimization

Design of laminated composites structures is becoming increasingly important as the use of composite materials steadily increases. This development is driven by the aerospace, automotive and wind turbine industries who need still lighter and stiffer/stronger structures. This presents a very challenging design task that calls upon structural optimization tools for providing basic design ideas. However, existing methods for handling laminated composites suffer from problems with local optima when optimizing the fiber orientation, which is the key to efficient design with laminated composites. To counter this problem Discrete Material Optimization (DMO) was suggested in [1] where an alternative parametrization of the optimization problem is used, inspired by the procedures in topology optimization. The idea is to discretize the problem by using only a limited number of pre-defined candidate fiber orientations, each described by a constitutive matrix, Ci. The optimization problem is then parameterized on the element level by expressing the constitutive matrix for lamina j as \( C_j = \sum _i x_{ij} C_i \) where \( \forall x_{ij} \in \left\{ {0,1} \right\} \) are the design variables for material i in lamina j. The objective of the optimization is then to choose one distinct material from the set of candidates, i.e. \( \sum _i x_{ij} = 1,\forall j \). The design variables, xij, may be associated with a specific lamina/element or a patch consisting of several laminae/elements, thereby significantly reducing the total number of design variables. The constitutive matrices,Ci, may represent any type of material, allowing for simultaneously optimization for fiber orientation and material choice.

Designing Sandwich Inserts and Core Junctions for Maximum Structural Stiffness Using Discrete Material Optimization

In the present paper the structural optimization approach Discrete Material Optimization (DMO) is introduced and applied to stiffness maximization of locally reinforced sandwich structures. The aim of the optimization is for each element to choose the material from the set of candidate materials that minimizes the objective the most. A design study of a sandwich panel in three-point bending shows that the DMO method is successful in providing valuable clues to efficient design of such structures.